Yep, that can happen.
If you like to push hard when singing, but it's making you go sharp, one thing you can try is to increase the level of bass in the headphone mix while you are doing the vocals. That's because because we perceive loud bass to be flatter than it is, and pitch ourselves accordingly.
If you are accustomed to singing live in loud situations, you (hopefully) learn to compensate for this, and adjust accordingly (by singing what seems to be a bit sharp). When you go into a studio and record, and if the general listening level is a lot quieter, that compensatory habit makes you go sharp.